A Hemispherical bowl, radius `r`, just full of water, will exert a total force down equal to the sum of all forces acting on the surface.
Total force down = area x pressure intensity at centroid
=`2pir^2 *"density of water"*"depth of centroid"*g`
= `2pir^2*rho*(r/2)g`
=`pir^3rhog`
But the forces acting around the hemispherical centroid balance out on opposite sides of the vertical axis and:
Resultant Force Down = volume of hemisphere * density of water * `g`
= `2/3pir^3rhog`